Big Hand, Small Pot Part 1: The Mistake

This is part one of two of the antithesis to Dan Skolovy's recent strategy article "Big Hand, Big Pot; Small Hand, Small Pot."

To prep yourself for the discussion to follow, check out the article here.

Now: How many times have you heard someone say "With pocket aces, you either win a small pot or lose a big one"?

If you've never heard it before, just wait. I promise you this will not be the only time you'll hear such a claim.

At the same time, you'll have the same players who espouse this maxim playing random any-two low cards into multi-way raised pots, under the theory:

"Players only raise, and call raises, with big cards, so there's a better chance these small ones will hit the flop and crush the big-card hands."

There are elements of truth to both of these statements. In fact, both statements have enough truth that I feel it's incorrect to pronounce them "incorrect."

However, it's my goal in this article to try and point out the holes in this logic and how they came to be.

The Setup

For the entirety of this article, we'll be using the following hypothetical situation:

We're in a cash game with 10 players. The Hero is a TAG (tight-aggressive) player and has a table image to match.

The other players are all solid, with no gamblers or hyper-aggressive personalities among them. Everyone has a healthy medium to deep stack.

We're going to classify a big hand as being only the top four hands for this discussion: AA, KK, QQ and JJ. A small hand is in the realm of low connectors and suited one-gappers.

Big drink, big pot?

Big Hand, Small Pot

The odds of getting dealt pocket aces are one in 221. Include the other three high pairs into this and you lower that to one in just over 55.

The odds of you getting one of these hands at the same time as another player become increasingly sparse (if anyone wants to do the math for me, throw it in a comment at the bottom of the page).

The vast majority of the times you're dealt one of these hands, none of your opponents will have a hand that makes it worthwhile putting any serious money in the pot.

When players have a hand worth seeing a flop with, such as a low pocket pair, they're going to miss hitting a set on the flop close to 87% of the time, making for a fold on the flop.

So for the vast majority of the times we are dealt a big hand, we'll win very small pots. The remainder of the time, your opponent will have a hand worth putting money into.

In these scenarios the pots are going to be rather large.

It's impossible to generate numbers for how often you will win the pot here, because there are far too many factors in this scenario. One of these factors is a major contributor to the perpetuation of this theory.

Big mouth, big pot?

Till Death Do Us Part

Beginners have a tendency to get married to these hands.

In the situations where an opponent has the best hand, pre- or post-flop, the amateur in question is unable to fold. They'll put all their money in to lose very large pots with these big hands.

In cases where the hand does hold up, the best-case scenario is you're up against an opponent like this, who's married to their hand. On other occasions you will be up against a stronger player who is able to fold.

If every time you lose, you lose a stack, and you only win a stack half the time you win, you're going to feel, rightfully so, that you're losing more than you are making.

The final factor is best summed up in a line straight out of Rounders:

"In Confessions of a Winning Poker Player," Jack King says, "few players recall big pots they have won, strange as it seems, but every player can remember with remarkable accuracy the outstanding tough beats of his career."

The players who believe in this theory are the same players who forget the majority of the times they did win a big pot with the big hand and remember all the losses.

Put these two factors together and you have a theory that seems irrefutable.

As Dan Skolovy mentioned in his article, you should be playing for stacks with big hands. This advice is dead-on accurate, but is only applicable to stronger players.

The 4/221 is accurate. At this point, each other player's odds of having pocket JJ, QQ, KK is ... (12/50) x (3/49)

To simplify the math, for every player to NOT have pocket JJ, QQ, KK; the formula should be: [ 1 - (12/50)x(3/49) ]^9 at a full table, with 9 representing the number of players. Subtracting this number from 1 leaves you with ~ 12.47% chance of an opponent holding JJ, QQ, or KK.

I may have made a grave error in logic here. Can someone discredit this formula?

Clips 2010-01-25 02:03:16

Crackmigg,

Thanks for the maths on this. I think it works heads-up, but it might be a different story when you're playing agains more than one opponent.

I don't know how to calculate those ones; if you feel like having a crack, I'd be keen to see what you come up with.

Max 2009-02-06 13:04:00

Its the definition of irony that when you read "With pocket aces, you either win a small pot or lose a big one"? you get dealt a-a in the poker game your playing and then lose your entire stack because somebody hit a set with pocket 10's on the turn with two other people in the pot :(. I spose it serves me right for reading on the internet as i play poker :S

crackmigg 2008-07-01 11:30:00

Here's the requested math:

There are (52*51):2 = 1326 ways of being dealt two cards. 3! = 6 of them are any pocket pair, so AA, KK, QQ, JJ are a combined 24:1326 = 4:221.

For the second player there are (50*49):2 = 1225 ways of being dealt two of the remaining cards. Assuming one of the top PP is out of the deck, there are 3*6 + 1 = 19 combinations of AA, KK, QQ, JJ remaining, so the odds are 19:1225 or 3.43:221.

Combined this has a chance of 4:221 * 3.43*221 = 1:3562 or about 0,00028%.

Sean Lind 2008-04-04 20:08:00

haha yeah, dyslexia, typo... something like that.

I even said in an earlier version that the 55 (55.25) was exactly one quarter of the Aces (makes sense, 4 hands = 4 times as likely as 1 hand).

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